We develop a model of amoeboid cell motility based on active gel theory. Modeling the motile apparatus of a eukaryotic cell as a confined layer of finite length of poroelastic active gel permeated by a solvent, we first show that, due to active stress and gel turnover, an initially static and homogeneous layer can undergo a contractile-type instability to a polarized moving state in which the rear is enriched in gel polymer. This agrees qualitatively with motile cells containing an actomyosin-rich uropod at their rear. We find that the gel layer settles into a steadily moving, inhomogeneous state at long times, sustained by a balance between contractility and filament turnover. In addition, our model predicts an optimal value of the gel-susbstrate adhesion leading to maximum layer speed, in agreement with cell motility assays. The model may be relevant to motility of cells translocating in complex, confining environments that can be mimicked experimentally by cell migration through microchannels.

Precisely how malaria parasites exit from infected red blood cells to further spread the disease remains poorly understood. It has been shown recently, however, that these parasites exploit the elasticity of the cell membrane to enable their egress. Based on this work, showing that parasites modify the membrane's spontaneous curvature, initiating pore opening and outward membrane curling, we develop a model of the dynamics of the red blood cell membrane leading to complete parasite egress. As a result of the three-dimensional, axisymmetric nature of the problem, we find that the membrane dynamics involve two modes of elastic-energy release: 1), at short times after pore opening, the free edge of the membrane curls into a toroidal rim attached to a membrane cap of roughly fixed radius; and 2), at longer times, the rim radius is fixed, and lipids in the cap flow into the rim. We compare our model with the experimental data of Abkarian and co-workers and obtain an estimate of the induced spontaneous curvature and the membrane viscosity, which control the timescale of parasite release. Finally, eversion of the membrane cap, which liberates the remaining parasites, is driven by the spontaneous curvature and is found to be associated with a breaking of the axisymmetry of the membrane.

We consider the curling of an initially flat but naturally curved elastica on a hard, nonadhesive surface. Combining theory, simulations, and experiments, we find novel behavior, including a constant front velocity and a self-similar shape of the curl that scales in size as t1/3 at long times after the release of one end of the elastica. The front velocity is selected by matching the self-similar solution with a roll of nearly constant curvature located near the free end.

Nature of curvature coupling of amphiphysin with membranes depends on its bound density

Cells are populated by a vast array of membrane-binding proteins that execute critical functions. Functions, like signaling and intracellular transport, require the abilities to bind to highly curved membranes and to trigger membrane deformation. Among these proteins is amphiphysin 1, implicated in clathrin-mediated endocytosis. It contains a Bin-Amphiphysin-Rvs membrane-binding domain with an N-terminal amphipathic helix that senses and generates membrane curvature. However, an understanding of the parameters distinguishing these two functions is missing. By pulling a highly curved nanotube of controlled radius from a giant vesicle in a solution containing amphiphysin, we observed that the action of the protein depends directly on its density on the membrane. At low densities of protein on the nearly flat vesicle, the distribution of proteins and the mechanical effects induced are described by a model based on spontaneous curvature induction. The tube radius and force are modified by protein binding but still depend on membrane tension. In the dilute limit, when practically no proteins were present on the vesicle, no mechanical effects were detected, but strong protein enrichment proportional to curvature was seen on the tube. At high densities, the radius is independent of tension and vesicle protein density, resulting from the formation of a scaffold around the tube. As a consequence, the scaling of the force with tension is modified. For the entire density range, protein was enriched on the tube as compared to the vesicle. Our approach shows that the strength of curvature sensing and mechanical effects on the tube depends on the protein density.